My only programming experience is with the Arduino so this is probably a stupid question. Is it feasible to port a C library written for a PIC18f2620 to the Arduino environment? Or would I be better off learning to program the PIC?
Depends on what library and what is your goal.
What library are you planning to port? Some may be ported over without any hassle at all (if there are no hardware registers being called). Although, chances are that the library allows you to do something with the specific hardware of the PIC.
Now, if the same hardware exists in the Arduino chip you have, then you need to both understand what the PIC code does and which registers to access in the ATmega328 to perform the same task.
What is your goal towards learning new things? A new family of chips? C for microcontrollers? How to use the internal peripherals in modern microcontrollers?